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Question

alex-rudenkiy

Asked:2020-08-22 00:53:18 +0000 UTC2020-08-22 00:53:18 +0000 UTC 2020-08-22 00:53:18 +0000 UTC

使用勾股定理训练神经网络

772

我想教神经网络勾股定理。一切似乎都正确完成，标准化数据，模型正确，但不清楚错误是什么..

import numpy as np

from keras.models import Sequential
from keras.layers.core import Dense, Activation
from keras.utils import np_utils

np.random.seed()

NB_EPOCH = 500
VERBOSE = 1

X_in = [[ 0 , 44 ], [ 0 , 18 ], [ 38 , 0 ], [ 48 , 14 ], [ 0 , 36 ], [ 14 , 0 ], [ 34 , 0 ], [ 0 , 0 ], [ 0 , 38 ], [ 32 , 0 ], [ 28 , 0 ], [ 36 , 0 ], [ 20 , 48 ], [ 0 , 6 ], [ 0 , 20 ], [ 0 , 42 ], [ 0 , 8 ], [ 24 , 32 ], [ 4 , 0 ], [ 6 , 8 ], [ 24 , 10 ], [ 0 , 22 ], [ 16 , 12 ], [ 30 , 40 ], [ 0 , 32 ], [ 0 , 32 ], [ 16 , 0 ], [ 48 , 20 ], [ 0 , 8 ], [ 32 , 0 ], [ 0 , 46 ], [ 0 , 22 ], [ 0 , 8 ], [ 10 , 24 ], [ 0 , 36 ], [ 14 , 0 ], [ 0 , 22 ], [ 42 , 0 ], [ 16 , 12 ], [ 40 , 30 ], [ 44 , 0 ], [ 40 , 0 ], [ 34 , 0 ], [ 0 , 32 ], [ 40 , 30 ], [ 32 , 0 ], [ 0 , 30 ], [ 24 , 18 ], [ 0 , 26 ], [ 22 , 0 ], [ 0 , 4 ], [ 16 , 0 ], [ 10 , 0 ], [ 0 , 32 ], [ 0 , 42 ], [ 2 , 0 ], [ 0 , 38 ], [ 32 , 24 ], [ 48 , 0 ], [ 20 , 0 ], [ 0 , 18 ], [ 0 , 38 ], [ 14 , 48 ], [ 40 , 42 ], [ 16 , 12 ], [ 26 , 0 ], [ 0 , 20 ], [ 40 , 30 ], [ 16 , 30 ], [ 36 , 48 ], [ 36 , 0 ], [ 18 , 24 ], [ 34 , 0 ], [ 16 , 0 ], [ 0 , 24 ], [ 0 , 24 ], [ 0 , 18 ], [ 38 , 0 ], [ 28 , 0 ], [ 0 , 34 ], [ 0 , 36 ], [ 24 , 32 ], [ 16 , 30 ], [ 40 , 30 ], [ 24 , 0 ], [ 0 , 14 ], [ 8 , 6 ], [ 12 , 0 ], [ 16 , 0 ], [ 16 , 30 ], [ 48 , 14 ], [ 0 , 30 ], [ 38 , 0 ], [ 38 , 0 ], [ 0 , 8 ], [ 36 , 48 ], [ 0 , 32 ], [ 10 , 24 ], [ 46 , 0 ], [ 24 , 10 ], [ 30 , 0 ], [ 0 , 48 ], [ 40 , 0 ], [ 42 , 0 ], [ 32 , 24 ], [ 32 , 0 ], [ 12 , 16 ], [ 0 , 4 ], [ 0 , 28 ], [ 32 , 0 ], [ 40 , 42 ], [ 46 , 0 ], [ 0 , 24 ], [ 30 , 16 ], [ 36 , 48 ], [ 40 , 0 ], [ 24 , 0 ], [ 0 , 22 ], [ 40 , 42 ], [ 10 , 24 ], [ 0 , 16 ], [ 14 , 48 ], [ 22 , 0 ], [ 0 , 22 ], [ 30 , 0 ], [ 0 , 2 ], [ 48 , 20 ], [ 6 , 0 ], [ 6 , 0 ], [ 28 , 0 ], [ 20 , 0 ], [ 0 , 40 ], [ 42 , 0 ], [ 48 , 36 ], [ 14 , 0 ], [ 10 , 24 ], [ 0 , 30 ], [ 48 , 20 ], [ 40 , 30 ], [ 0 , 0 ], [ 42 , 40 ], [ 0 , 48 ], [ 32 , 24 ]]
X_answer = [[44] ,[18] ,[38] ,[50] ,[36] ,[14] ,[34] ,[0] ,[38] ,[32] ,[28] ,[36] ,[52] ,[6] ,[20] ,[42] ,[8] ,[40] ,[4] ,[10] ,[26] ,[22] ,[20] ,[50] ,[32] ,[32] ,[16] ,[52] ,[8] ,[32] ,[46] ,[22] ,[8] ,[26] ,[36] ,[14] ,[22] ,[42] ,[20] ,[50] ,[44] ,[40] ,[34] ,[32] ,[50] ,[32] ,[30] ,[30] ,[26] ,[22] ,[4] ,[16] ,[10] ,[32] ,[42] ,[2] ,[38] ,[40] ,[48] ,[20] ,[18] ,[38] ,[50] ,[58] ,[20] ,[26] ,[20] ,[50] ,[34] ,[60] ,[36] ,[30] ,[34] ,[16] ,[24] ,[24] ,[18] ,[38] ,[28] ,[34] ,[36] ,[40] ,[34] ,[50] ,[24] ,[14] ,[10] ,[12] ,[16] ,[34] ,[50] ,[30] ,[38] ,[38] ,[8] ,[60] ,[32] ,[26] ,[46] ,[26] ,[30] ,[48] ,[40] ,[42] ,[40] ,[32] ,[20] ,[4] ,[28] ,[32] ,[58] ,[46] ,[24] ,[34] ,[60] ,[40] ,[24] ,[22] ,[58] ,[26] ,[16] ,[50] ,[22] ,[22] ,[30] ,[2] ,[52] ,[6] ,[6] ,[28] ,[20] ,[40] ,[42] ,[60] ,[14] ,[26] ,[30] ,[52] ,[50] ,[0] ,[58] ,[48] ,[40]]
X_in = np.asarray(X_in, dtype=np.float32)
X_answer = np.asarray(X_answer, dtype=np.float32)

X_in /= np.amax(X_in)
X_answer /= np.amax(X_answer)

model = Sequential()
model.add(Dense(10, input_dim = 2, activation='relu'))
model.add(Dense(10, activation='relu'))
model.add(Dense(1, activation='softmax'))

model.compile(loss='mean_squared_error', optimizer='adam', metrics=['accuracy'])

history = model.fit(X_in, X_answer, epochs=NB_EPOCH, verbose=VERBOSE)

对于 100 个 epoch，对于 500 个相同的结果：

Epoch 1/100
143/143 [==============================] - 0s 2ms/step - loss: 0.2966 - acc: 0.0280
Epoch 2/100
143/143 [==============================] - 0s 52us/step - loss: 0.2966 - acc: 0.0280
Epoch 3/100
143/143 [==============================] - 0s 52us/step - loss: 0.2966 - acc: 0.0280
Epoch 4/100
143/143 [==============================] - 0s 38us/step - loss: 0.2966 - acc: 0.0280
Epoch 5/100
143/143 [==============================] - 0s 52us/step - loss: 0.2966 - acc: 0.0280
Epoch 6/100
143/143 [==============================] - 0s 45us/step - loss: 0.2966 - acc: 0.0280
Epoch 7/100
143/143 [==============================] - 0s 45us/step - loss: 0.2966 - acc: 0.0280
Epoch 8/100
143/143 [==============================] - 0s 42us/step - loss: 0.2966 - acc: 0.0280
Epoch 9/100
143/143 [==============================] - 0s 45us/step - loss: 0.2966 - acc: 0.0280
Epoch 10/100
143/143 [==============================] - 0s 42us/step - loss: 0.2966 - acc: 0.0280
Epoch 11/100
143/143 [==============================] - 0s 38us/step - loss: 0.2966 - acc: 0.0280
Epoch 12/100
143/143 [==============================] - 0s 45us/step - loss: 0.2966 - acc: 0.0280
Epoch 13/100
143/143 [==============================] - 0s 42us/step - loss: 0.2966 - acc: 0.0280
Epoch 14/100
143/143 [==============================] - 0s 42us/step - loss: 0.2966 - acc: 0.0280
Epoch 15/100
143/143 [==============================] - 0s 42us/step - loss: 0.2966 - acc: 0.0280
Epoch 16/100
143/143 [==============================] - 0s 45us/step - loss: 0.2966 - acc: 0.0280
Epoch 17/100
143/143 [==============================] - 0s 38us/step - loss: 0.2966 - acc: 0.0280
Epoch 18/100
143/143 [==============================] - 0s 38us/step - loss: 0.2966 - acc: 0.0280
Epoch 19/100
143/143 [==============================] - 0s 42us/step - loss: 0.2966 - acc: 0.0280
Epoch 20/100
143/143 [==============================] - 0s 35us/step - loss: 0.2966 - acc: 0.0280
Epoch 21/100
143/143 [==============================] - 0s 45us/step - loss: 0.2966 - acc: 0.0280
Epoch 22/100
143/143 [==============================] - 0s 42us/step - loss: 0.2966 - acc: 0.0280
Epoch 23/100
143/143 [==============================] - 0s 35us/step - loss: 0.2966 - acc: 0.0280
Epoch 24/100
143/143 [==============================] - 0s 45us/step - loss: 0.2966 - acc: 0.0280
Epoch 25/100
143/143 [==============================] - 0s 38us/step - loss: 0.2966 - acc: 0.0280
Epoch 26/100
143/143 [==============================] - 0s 42us/step - loss: 0.2966 - acc: 0.0280
Epoch 27/100
143/143 [==============================] - 0s 42us/step - loss: 0.2966 - acc: 0.0280
Epoch 28/100
143/143 [==============================] - 0s 45us/step - loss: 0.2966 - acc: 0.0280
Epoch 29/100
143/143 [==============================] - 0s 45us/step - loss: 0.2966 - acc: 0.0280
Epoch 30/100
143/143 [==============================] - 0s 45us/step - loss: 0.2966 - acc: 0.0280
Epoch 31/100
143/143 [==============================] - 0s 45us/step - loss: 0.2966 - acc: 0.0280
Epoch 32/100
143/143 [==============================] - 0s 52us/step - loss: 0.2966 - acc: 0.0280
Epoch 33/100
143/143 [==============================] - 0s 42us/step - loss: 0.2966 - acc: 0.0280
Epoch 34/100
143/143 [==============================] - 0s 45us/step - loss: 0.2966 - acc: 0.0280
Epoch 35/100
143/143 [==============================] - 0s 38us/step - loss: 0.2966 - acc: 0.0280
Epoch 36/100
143/143 [==============================] - 0s 42us/step - loss: 0.2966 - acc: 0.0280
Epoch 37/100
143/143 [==============================] - 0s 49us/step - loss: 0.2966 - acc: 0.0280
Epoch 38/100
143/143 [==============================] - 0s 38us/step - loss: 0.2966 - acc: 0.0280
Epoch 39/100
143/143 [==============================] - 0s 45us/step - loss: 0.2966 - acc: 0.0280
Epoch 40/100
143/143 [==============================] - 0s 42us/step - loss: 0.2966 - acc: 0.0280
Epoch 41/100
143/143 [==============================] - 0s 42us/step - loss: 0.2966 - acc: 0.0280
Epoch 42/100
143/143 [==============================] - 0s 38us/step - loss: 0.2966 - acc: 0.0280
Epoch 43/100
143/143 [==============================] - 0s 38us/step - loss: 0.2966 - acc: 0.0280
Epoch 44/100
143/143 [==============================] - 0s 45us/step - loss: 0.2966 - acc: 0.0280
Epoch 45/100
143/143 [==============================] - 0s 38us/step - loss: 0.2966 - acc: 0.0280
Epoch 46/100
143/143 [==============================] - 0s 45us/step - loss: 0.2966 - acc: 0.0280
Epoch 47/100
143/143 [==============================] - 0s 45us/step - loss: 0.2966 - acc: 0.0280
Epoch 48/100
143/143 [==============================] - 0s 42us/step - loss: 0.2966 - acc: 0.0280
Epoch 49/100
143/143 [==============================] - 0s 38us/step - loss: 0.2966 - acc: 0.0280
Epoch 50/100
143/143 [==============================] - 0s 42us/step - loss: 0.2966 - acc: 0.0280
Epoch 51/100
143/143 [==============================] - 0s 42us/step - loss: 0.2966 - acc: 0.0280
Epoch 52/100
143/143 [==============================] - 0s 42us/step - loss: 0.2966 - acc: 0.0280
Epoch 53/100
143/143 [==============================] - 0s 42us/step - loss: 0.2966 - acc: 0.0280
Epoch 54/100
143/143 [==============================] - 0s 42us/step - loss: 0.2966 - acc: 0.0280
Epoch 55/100
143/143 [==============================] - 0s 49us/step - loss: 0.2966 - acc: 0.0280
Epoch 56/100
143/143 [==============================] - 0s 45us/step - loss: 0.2966 - acc: 0.0280
Epoch 57/100
143/143 [==============================] - 0s 38us/step - loss: 0.2966 - acc: 0.0280
Epoch 58/100
143/143 [==============================] - 0s 45us/step - loss: 0.2966 - acc: 0.0280
Epoch 59/100
143/143 [==============================] - 0s 35us/step - loss: 0.2966 - acc: 0.0280
Epoch 60/100
143/143 [==============================] - 0s 42us/step - loss: 0.2966 - acc: 0.0280
Epoch 61/100
143/143 [==============================] - 0s 35us/step - loss: 0.2966 - acc: 0.0280
Epoch 62/100
143/143 [==============================] - 0s 38us/step - loss: 0.2966 - acc: 0.0280
Epoch 63/100
143/143 [==============================] - 0s 38us/step - loss: 0.2966 - acc: 0.0280
Epoch 64/100
143/143 [==============================] - 0s 38us/step - loss: 0.2966 - acc: 0.0280
Epoch 65/100
143/143 [==============================] - 0s 52us/step - loss: 0.2966 - acc: 0.0280
Epoch 66/100
143/143 [==============================] - 0s 38us/step - loss: 0.2966 - acc: 0.0280
Epoch 67/100
143/143 [==============================] - 0s 45us/step - loss: 0.2966 - acc: 0.0280
Epoch 68/100
143/143 [==============================] - 0s 38us/step - loss: 0.2966 - acc: 0.0280
Epoch 69/100
143/143 [==============================] - 0s 52us/step - loss: 0.2966 - acc: 0.0280
Epoch 70/100
143/143 [==============================] - 0s 42us/step - loss: 0.2966 - acc: 0.0280
Epoch 71/100
143/143 [==============================] - 0s 42us/step - loss: 0.2966 - acc: 0.0280
Epoch 72/100
143/143 [==============================] - 0s 45us/step - loss: 0.2966 - acc: 0.0280
Epoch 73/100
143/143 [==============================] - 0s 39us/step - loss: 0.2966 - acc: 0.0280
Epoch 74/100
143/143 [==============================] - 0s 42us/step - loss: 0.2966 - acc: 0.0280
Epoch 75/100
143/143 [==============================] - 0s 38us/step - loss: 0.2966 - acc: 0.0280
Epoch 76/100
143/143 [==============================] - 0s 45us/step - loss: 0.2966 - acc: 0.0280
Epoch 77/100
143/143 [==============================] - 0s 42us/step - loss: 0.2966 - acc: 0.0280
Epoch 78/100
143/143 [==============================] - 0s 49us/step - loss: 0.2966 - acc: 0.0280
Epoch 79/100
143/143 [==============================] - 0s 38us/step - loss: 0.2966 - acc: 0.0280
Epoch 80/100
143/143 [==============================] - 0s 49us/step - loss: 0.2966 - acc: 0.0280
Epoch 81/100
143/143 [==============================] - 0s 42us/step - loss: 0.2966 - acc: 0.0280
Epoch 82/100
143/143 [==============================] - 0s 35us/step - loss: 0.2966 - acc: 0.0280
Epoch 83/100
143/143 [==============================] - 0s 42us/step - loss: 0.2966 - acc: 0.0280
Epoch 84/100
143/143 [==============================] - 0s 35us/step - loss: 0.2966 - acc: 0.0280
Epoch 85/100
143/143 [==============================] - 0s 42us/step - loss: 0.2966 - acc: 0.0280
Epoch 86/100
143/143 [==============================] - 0s 38us/step - loss: 0.2966 - acc: 0.0280
Epoch 87/100
143/143 [==============================] - 0s 38us/step - loss: 0.2966 - acc: 0.0280
Epoch 88/100
143/143 [==============================] - 0s 42us/step - loss: 0.2966 - acc: 0.0280
Epoch 89/100
143/143 [==============================] - 0s 38us/step - loss: 0.2966 - acc: 0.0280
Epoch 90/100
143/143 [==============================] - 0s 49us/step - loss: 0.2966 - acc: 0.0280
Epoch 91/100
143/143 [==============================] - 0s 38us/step - loss: 0.2966 - acc: 0.0280
Epoch 92/100
143/143 [==============================] - 0s 45us/step - loss: 0.2966 - acc: 0.0280
Epoch 93/100
143/143 [==============================] - 0s 38us/step - loss: 0.2966 - acc: 0.0280
Epoch 94/100
143/143 [==============================] - 0s 45us/step - loss: 0.2966 - acc: 0.0280
Epoch 95/100
143/143 [==============================] - 0s 42us/step - loss: 0.2966 - acc: 0.0280
Epoch 96/100
143/143 [==============================] - 0s 42us/step - loss: 0.2966 - acc: 0.0280
Epoch 97/100
143/143 [==============================] - 0s 42us/step - loss: 0.2966 - acc: 0.0280
Epoch 98/100
143/143 [==============================] - 0s 45us/step - loss: 0.2966 - acc: 0.0280
Epoch 99/100
143/143 [==============================] - 0s 42us/step - loss: 0.2966 - acc: 0.0280
Epoch 100/100
143/143 [==============================] - 0s 38us/step - loss: 0.2966 - acc: 0.0280

2 个回答

Voted

L. Murashov · Answer 1 · 2020-08-22T01:28:47Z

L. Murashov

2020-08-22T01:28:47Z2020-08-22T01:28:47Z

你在最后一层有错误的激活函数。Softmax 受限 [0..1]

model.add(Dense(1, activation='softmax'))

取而代之

# После слоя не применяется функция активации
model.add(Dense(1))

此外，准确性在这里毫无用处。回归任务。

metrics=['accuracy']

3

MaxU - stop genocide of UA · Answer 2 · 2020-08-22T05:18:06Z

正如@L.Murashov已经说过的那样，激活函数softmax用于多类分类问题 - 它有助于计算样本属于每个类的概率。

还有几点需要注意：

训练样本中有太多（大约一半）零值 - 这是勾股定理的退化情况，当三角形的一条边的长度为零时。
为了更好地训练模型，您可以采用更大的样本 - 在您的情况下，生成所需的尽可能多的数据不是问题。
对于这个（简单）任务，一个隐藏层就足够了
作为输出层的激活函数，可以使用linear
作为损失和度量的函数，您可以选择mean_squared_error

例子：

import numpy as np
from keras.models import Sequential
from keras.layers.core import Dense, Activation

N = 5000
np.random.seed(1234)
X = np.random.randint(0, 50, size=(N,2))
y = np.linalg.norm(X, axis=1)

NB_EPOCHS = 100
VERBOSE = 1

model = Sequential()
model.add(Dense(20, input_dim = 2, activation='relu'))
model.add(Dense(1, activation='linear'))
model.compile(loss='mse', optimizer='adam', metrics=['mean_squared_error'])
model.fit(X, y, epochs=NB_EPOCHS, verbose=VERBOSE)

教育：

...
5000/5000 [==============================] - 0s 22us/step - loss: 0.0057 - mean_squared_error: 0.0057
Epoch 98/100
5000/5000 [==============================] - 0s 22us/step - loss: 0.0048 - mean_squared_error: 0.0048
Epoch 99/100
5000/5000 [==============================] - 0s 22us/step - loss: 0.0045 - mean_squared_error: 0.0045
Epoch 100/100
5000/5000 [==============================] - 0s 22us/step - loss: 0.0043 - mean_squared_error: 0.0043
Out[70]: <keras.callbacks.History at 0xf2d9ac8>

预言：

In [71]: model.predict(np.array([[3,4], [10,10], [5,6]]))
Out[71]:
array([[ 5.018393],
       [14.130004],
       [ 7.841759]], dtype=float32)

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2 个回答

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